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Journal of Physics A Mathematical and General

An analytical description of the low temperature behaviour of a weakly interacting Bose gas

Guozhen Su, Lixuan Chen, Jincan Chen

Published Feb 11, 2004• 4 citations
Publisher

Abstract

An analytical description of the low temperature behaviour of a trapped interacting Bose gas is presented by using a simple approach that is based on the principle of the constancy of chemical potentials in equilibrium and the local-density approximation. Several thermodynamic quantities, which include the ground-state fraction, chemical potential, total energy, entropy and heat capacity, are derived analytically. It is shown that the results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation. Meanwhile, by selecting a suitable variable, the divergent problem existing in some papers is solved.

DOI
10.1088/0305-4470/37/8/014

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An analytical description of the low temperature behaviour of a trapped interacting Bose gas is presented by using a simple approach that is based on the principle of the constancy of chemical potentials in equilibrium and the local-density approximation. Several thermodynamic quantities, which include the ground-state fraction, chemical potential, total energy, entropy and heat capacity, are derived analytically. It is shown that the results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation. Meanwhile, by selecting a suitable variable, the divergent problem existing in some papers is solved.
In this work, we build upon the theoretical framework developed in our previous study [N. V. Thu and D. T. Pham, Phys. Lett. A 523, 129787 (2024)], where the Cornwall–Jackiw–Tomboulis effective action formalism was applied to a dilute Bose gas, to investigate its thermodynamic properties in the condensed phase at sufficiently low temperatures within the improved Hartree–Fock approximation. We focus on the analyses of the chemical potential, pressure, energy density and specific heat at constant volume, which are derived within a unified, self-consistent and gapless framework. The results obtained show excellent agreement with those predicted by the Hartree–Fock–Bogoliubov theory in the appropriate limits. Remarkably, our results demonstrate universal behavior for the reduced thermodynamic quantities, and a comparison with available experimental data for the chemical potential is made.
In this paper the thermodynamical parameters of a condensed Boson gas are calculated from the partial derivative of the grand potential. In particular, the analytical expressions for some important parameters, such as the condensed fraction, specific heat, critical temperature, effective size, and release energy are investigated. The mean effects which can be altered the ideal Bose gas, such as finite size, highly anisotropic of the external potential and interatomic interaction effects are considered simultaneously. Some new characteristics of the trapped interacting Bose gases in a highly anisotropic trap are revealed. The calculated result for the condensed fraction is compared with the ongoing Stuttgart experiment for 52Cr (Griesmaier et al., Phys. Rev. Lett. 94, 160401(2005)) directly. Good agreement between both the theoretical and experimental data are obtained.
The low-temperature properties of a weakly interacting Bose gas in weak magnetic field were studied by using the conclusions of local-density approximation method and invariability principle of chemical potential in inhomogenous system.The analytical expressions of the ground-state fraction,boundary magnetic potential in condensation region,chemical potential,total energy and heat capacity were derived.The effects of magnetic field and interparticle interactions on properties of the system were discussed.It is shown that when repulsive interactions are kept constant,the effects of variational magnetic filed on condensation volume,total energy and heat capacity of the system have boundary temperature respectively.The repulsive interactions make the chemical potential of the system always positive and increase with the decreasing temperature,the total energy of the system is lifted a platform and a maximum is obtained near condensation temperature;the heat capacity of the system have the reversal point and the maximum point with the changing temperature;and the total energy and heat capacity decrease rapidly from their own maximums with the temperature approaching to condensation temperature.